Constraints on an empirical flux equation for asymmetry-induced transport

Despite a large body of experimental work on asymmetry-induced transport, the correct theory remains elusive. We are currently developing an empirical model of the transport with an eye toward providing guidance for further theoretical development. In previous work\footnote{D.~L. Eggleston and J.~M. Williams, Phys. Plasmas 15, 032305 (2008).} we have shown that the flux equation for the transport is empirically constrained to be of the form $\Gamma(\epsilon) = -(B_0/B)^{1.33}D(\epsilon)[\nabla n_0+f(\epsilon)]$, where $\epsilon=\omega -l\omega_R$, $\omega$ is the asymmetry frequency, $\omega_R$ the plasma rotation frequency, $l$ the azimuthal mode number, $B$ the magnetic field, $n_0$ the density, $B_0$ an empirical constant, and $D (\epsilon)$ and $f(\epsilon)$ are unknown functions. To gain information about $D(\epsilon)$ and $f(\epsilon)$, we have examined data near the $\epsilon=0$ point and compared it to a first order expansion of $\Gamma(\epsilon)$. This analysis shows that $dD/d\epsilon(0)\not=0$, in contradiction to resonant particle theory\footnote{D.~L. Eggleston and T.~M. O'Neil, Phys. Plasmas 6, 2699 (1999).}. We also find that $f(\epsilon)$ can only be a fraction of the size predicted by that theory, and that $dD/d\epsilon(0)$ is an increasing function of radius and scales with the inverse of the center wire bias. This last result suggests that $\epsilon$ may be scaled by $\omega_R$ rather than the axial bounce frequency.